Nonlinear analysis of spacecraft thermal models

TL;DR

This paper analyzes nonlinear differential equations modeling spacecraft thermal behavior, demonstrating conditions for steady states and limit cycles, and introduces new numerical methods to enhance thermal analysis beyond commercial software capabilities.

Contribution

It extends nonlinear analysis techniques to complex spacecraft thermal models and proposes novel numerical methods for improved thermal behavior prediction.

Findings

Temperatures reach steady states under constant heat input.

Periodic heat input leads to limit cycle behavior.

New numerical approaches complement existing thermal analysis tools.

Abstract

We study the differential equations of lumped-parameter models of spacecraft thermal control. Firstly, we consider a satellite model consisting of two isothermal parts (nodes): an outer part that absorbs heat from the environment as radiation of various types and radiates heat as a black-body, and an inner part that just dissipates heat at a constant rate. The resulting system of two nonlinear ordinary differential equations for the satellite's temperatures is analyzed with various methods, which prove that the temperatures approach a steady state if the heat input is constant, whereas they approach a limit cycle if it varies periodically. Secondly, we generalize those methods to study a many-node thermal model of a spacecraft: this model also has a stable steady state under constant heat inputs that becomes a limit cycle if the inputs vary periodically. Finally, we propose new numerical analyses of spacecraft thermal models based on our results, to complement the analyses normally carried out with commercial software packages.